Here are some papers for addressing limitations of the Metropolis Light Transport algorithm.
Flickering in animations
The remedy to this limitation is to mutate paths through both space and time, not just space.
Physically-based Animation Rendering with Markov Chain Monte Carlo
Poor SIMD efficiency
The remedy to this to have multiple proposals per iteration instead of one.
Coherent Metropolis Light Transport with Multiple-Try Mutations this paper uses multiple try metropolis and exploits the correlation between proposals to accelerate it with ray packets.
however since then more efficient multiple proposal metropolis algorithms such as the one i posted in the Useful Markov Chain Monte Carlo Papers to apply to Graphics
Outliers(aka. Fireflies, Bright spots)
The unbiased remedy to this is to ensure that there is a way of finding a point that gets accepted within a few iterations. first of all use the right proposal distribution such as such as a robust mutation strategy(such as The Natural-Constraint Representation of the Path Space for Efficient Light Transport Simulation and A Simple and Robust Mutation Strategy for the Metropolis Light Transport Algorithm) and choose the right step size, an Adaptive Markov Chain Monte Carlo method(see the Useful Markov Chain Monte Carlo Papers to apply to Graphics
Post for papers on this topic) is an automatic way of doing this. second of all use multiple proposals to increase the chance that one of them gets accepted. and as a last resort use a form of parallel tempering between the actual importance function and one with flatter peaks(such as in Replica exchange light transport on relaxed distributions) or no peaks(such as in Robust Adaptive Photon Tracing using Photon Path Visibility).
Lack of Stratification
The remedies to this include using Markov Chain Quasi Monte Carlo methods(see the Useful Markov Chain Monte Carlo Papers to apply to Graphics
Post for papers on this topic),a good mutation strategy (such as in The Natural-Constraint Representation of the Path Space for Efficient Light Transport Simulation) , a importance function such as luminance relative to each individual pixel or variance(such as in Arbitrary Importance Functions for Metropolis Light Transport), having multiple proposals in each iteration placed in a stratified manner (such as in Acceleration of the Multiple-Try Metropolis algorithm using antithetic and stratified sampling).
Must read and other references.
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